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Quantum de Finetti Theorem under Fully-One-Way Adaptive Measurements
Ke Li1,2, Graeme Smith1
1IBM T.J. Watson Research Center, Yorktown Heights, New York 10598, USA.
Physical Review Letters
|May 9, 2015
Summary
Quantum states invariant under permutation are approximated by mixtures of product states. This finding enhances quantum de Finetti theorems using one-way local operations and classical communication (LOCC) for measurement-based approximation.
Area of Science:
- Quantum Information Theory
- Quantum Many-Body Physics
Background:
- The quantum de Finetti theorem relates properties of many-particle quantum systems to simpler, independent systems.
- Permutation-invariant quantum states are fundamental in quantum information processing.
Purpose of the Study:
- To prove a version of the quantum de Finetti theorem for permutation-invariant states.
- To establish approximation guarantees using fully-one-way local operations and classical communication (LOCC).
Main Methods:
- Developing a novel quantum de Finetti theorem.
- Utilizing distinguishability measures under specific quantum measurement constraints (fully-one-way LOCC).
Main Results:
- Demonstrated that permutation-invariant quantum states can be approximated by probabilistic mixtures of multifold product states.
- Strengthened existing de Finetti theorems by employing a more restrictive measurement model (fully-one-way LOCC).
Conclusions:
- The study provides a refined understanding of quantum state approximation and its implications for quantum information.
- Established a quasipolynomial-time algorithm for detecting multipartite entanglement and proved limitations on the power of multiple provers in quantum proof systems under LOCC restrictions.
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